Superconductivity and phonon softening. III. Relation between electron bands and phonons in Nb, Mo, and their alloys

Calculations are presented by ${\ensuremath{\chi}}_{1}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}})$ and ${\ensuremath{\chi}}_{2}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}},\ensuremath{\omega})$ for Nb, Mo, and alloys in the rigid-band model. The matrix elements are set to 1. The results for Nb agree with a previous calculation by Cooke, Davis, and Mostoller. An empirical linear relation is found between ${\ensuremath{\chi}}_{1}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}})$ and $\frac{d{\ensuremath{\chi}}_{2}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}},0)}{d\ensuremath{\omega}}$. This relation leads to a simple formula relating the superconducting coupling constant ($\ensuremath{\lambda}$) to the phonon frequencies. However, we are unable to evaluate the terms in this formula with sufficient accuracy to calculate $\ensuremath{\lambda}$.